Sensorless position estimation for interior permanent magnet synchronous motor

ABSTRACT

A sensorless position estimation and control system and method for a permanent magnet electric motor of a powertrain system of a vehicle involve determining a reference torque to be achieved by the electric motor based on a set of vehicle operating parameters, determining a reference current magnitude to achieve the determined reference torque using a lookup table, determining current commands for the electric motor based on the determined reference current magnitude and a fixed reference current angle, injecting a high frequency voltage into a voltage control loop for the electric motor and estimating, by the controller, a position of a rotor of the electric motor thereafter, and controlling a current provided to the electric motor based on the determined current commands and the estimated rotor position.

CROSS-REFERENCE TO RELATED APPLICATION

The present application claims the benefit of U.S. ProvisionalApplication No. 62/733,955, filed on Sep. 20, 2018. The disclosure ofthis application is incorporated herein by reference in its entirety.

FIELD

The present application generally relates to electric motors and, moreparticularly, to techniques for sensorless position estimation for aninterior permanent magnet synchronous motor (IPMSM).

BACKGROUND

A permanent magnet electric motor is a type of electric motor that usespermanent magnets rather than electromagnetic coils (also known as“field windings”) that are commonly found in an induction motor.Permanent magnet electric motors are desirable for as traction motorsfor electrified vehicles due to their high power density and efficiency.One specific type of permanent magnet electric motor is an interiorpermanent magnet synchronous motor (IPMSM). This type of motor haspermanent magnets embedded in the rotor laminations to create a magneticfield. It is necessary to track the position of the magnetic field andprecisely control current provided to the stator coils for maximizedperformance and efficiency. Position sensors, such as resolvers,encoders, Hall effect sensors, eddy current sensors, and the like, aretypically implemented to monitor rotor position. These devices, however,are costly and are sometimes potentially inaccurate. Accordingly, whilesuch motor control systems do work well for their intended purpose,there remains a need for improvement in the relevant art.

SUMMARY

According to one example aspect of the invention, a powertrain systemfor a vehicle is presented. In one exemplary implementation, the systemcomprises: a permanent magnet electric motor configured to generatedrive torque for propulsion of the vehicle and a controller configuredto: perform sensorless position estimation on the permanent magnetelectric motor by: (i) determining a reference torque to be achieved bythe electric motor based on a set of vehicle operating parameters, (ii)determining a reference current magnitude to achieve the determinedreference torque using a lookup table, (iii) determining currentcommands for the electric motor based on the determined referencecurrent magnitude and a fixed reference current angle, and (iv)injecting a high frequency voltage into a voltage control loop for theelectric motor and estimating a position of a rotor of the electricmotor thereafter, and control a current provided to the electric motorbased on the determined current commands and the estimated rotorposition.

In some implementations, the controller determines the current commandsfor the electric motor to achieve the determined reference torquewithout utilizing a complex maximum torque per amp (MTPA) table. In someimplementations, the controller obtains a compensation value that isapplied to an estimated rotor position error without utilizing multiplecomplex look-up tables (LUTs). In some implementations, the controllerdoes not utilize a position sensor to measure an actual position of therotor.

In some implementations, the determining of the reference currentmagnitude and the current commands based on the determined referencecurrent magnitude and a fixed reference current angle are performedacross all possible values of the determined reference torque so as tonot require an estimation/control strategy transition. In someimplementations, the determining of the reference current magnitude andthe current commands based on the determined reference current magnitudeand a fixed reference current angle are performed only when thedetermined reference torque exceeds a threshold. In someimplementations, when the determined reference torque is less than thethreshold, the controller is further configured to determine the currentcommands for the electric motor using a complex MTPA table.

According to another example aspect of the invention, a sensorlessposition estimation and control method for a permanent magnet electricmotor of a powertrain system of a vehicle is presented. In one exemplaryimplementation, the method comprises: determining, by a controller ofthe powertrain system, a reference torque to be achieved by the electricmotor based on a set of vehicle operating parameters, determining, bythe controller, a reference current magnitude to achieve the determinedreference torque using a lookup table, determining, by the controller,current commands for the electric motor based on the determinedreference current magnitude and a fixed reference current angle,injecting, by the controller, a high frequency voltage into a voltagecontrol loop for the electric motor and estimating, by the controller, aposition of a rotor of the electric motor thereafter, and controlling,by the controller, a current provided to the electric motor based on thedetermined current commands and the estimated rotor position.

In some implementations, determining the current commands for theelectric motor to achieve the determined reference torque is performedwithout utilizing a complex MTPA table. In some implementations,obtaining a compensation value that is applied to an estimated rotorposition error is performed without utilizing multiple complex LUTs. Insome implementations, the controller does not utilize a position sensorto measure an actual position of the rotor.

In some implementations, the determining of the reference currentmagnitude and the current commands based on the determined referencecurrent magnitude and a fixed reference current angle are performedacross all possible values of the determined reference torque so as tonot require an estimation/control strategy transition. In someimplementations, the determining of the reference current magnitude andthe current commands based on the determined reference current magnitudeand a fixed reference current angle are performed only when thedetermined reference torque exceeds a threshold. In someimplementations, when the determined reference torque is less than thethreshold, the method further comprises determining, by the controller,the current commands for the electric motor using a complex maximumtorque per amp MTPA table.

Further areas of applicability of the teachings of the presentdisclosure will become apparent from the detailed description, claimsand the drawings provided hereinafter, wherein like reference numeralsrefer to like features throughout the several views of the drawings. Itshould be understood that the detailed description, including disclosedembodiments and drawings referenced therein, are merely exemplary innature intended for purposes of illustration only and are not intendedto limit the scope of the present disclosure, its application or uses.Thus, variations that do not depart from the gist of the presentdisclosure are intended to be within the scope of the presentdisclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a functional block diagram of an example electrified vehiclehaving a permanent magnet electric motor according to the principles ofthe present disclosure;

FIG. 2 is a functional block diagram of an example sensorless positionestimation and control architecture for a permanent magnet electricmotor of an electrified vehicle according to the principles of thepresent disclosure;

FIGS. 3A-3B are plots of performance of compensation-based motorposition estimation and control technique and a fixed reference currentangle motor position estimation and control technique according to theprinciples of the present disclosure; and

FIG. 4 is a flow diagram of an example sensorless position estimationand control method for a permanent magnet electric motor of anelectrified vehicle according to the principles of the presentdisclosure.

DESCRIPTION

Referring now to FIG. 1, a functional block diagram of an exampleelectrified vehicle 100 (hereinafter, “vehicle 100”) is presented. Itwill be appreciated that the illustrated vehicle 100 is merely oneconfiguration of an interior permanent magnet (IPM) motor in anelectrified or hybrid vehicle and that the systems/methods of thepresent disclosure are applicable to any suitable IPM vehicleapplication. The vehicle 100 comprises a permanent magnet electric motor104 (hereinafter, “motor 100”) that generates drive torque, which istransferred to a driveline 108 via a transmission 112 to propel thevehicle 100. In one exemplary implementation, the motor 104 is aninterior permanent magnet synchronous motor (IPMSM). While an IPMSM forvehicle applications is specifically discussed herein, it will beappreciated that the sensorless position estimation techniques of thepresent disclosure could be applicable to non-vehicle applications aswell as other suitable permanent magnet electric motors, such as asurface permanent magnet synchronous motors (SPMSM) where the permanentmagnets are attached to the rotor lamination surface as opposed to beembedded therein like an IPMSM.

While a single motor 104 is illustrated and discussed herein, it willalso be appreciated that the vehicle 100 could include multiple motorsand/or an engine (not shown) for generating propulsive drive torque. Forexample only, the vehicle 100 could be an electrically all-wheel drive(eAWD) having the motor 104 coupled to one axle of the driveline 108 andan engine/transmission (an optionally, another electric motor, such as abelt-driven starter generator, or BSG unit) coupled to another axle ofthe driveline 108. A battery system 116 provides a current for poweringthe motor 104. A motor speed sensor 120 measures a rotational speed ofan output shaft 124 of the motor 104. A controller 128 controlsoperation of the vehicle 100, including controlling the current suppliedto the motor 104 to achieve a desired propulsive torque to meet a drivertorque demand (e.g., based on input via driver interface 132). Morespecifically, the controller 128 controls the current supplied to astator 136 (e.g., stator windings) of the motor 104, which varies amagnetic field that displaces a rotor 140 of the motor 104, which haspermanent magnets embedded in its laminations. The motor 104 and thecontroller 128 are also referred to collectively herein as “a powertrainsystem” of the vehicle 100.

The position of the rotor 140 is one factor in precisely controlling thestator current supply to achieve optimal motor performance andefficiency. As previously discussed, however, position sensors forpermanent magnet electric motors are expensive and sometimes areinaccurate. As a result, sensorless position estimation techniques forpermanent magnet electric motors are preferred. The benefits ofsensorless position estimation techniques include, but are not limitedto, decreased costs, decreased space/packaging (the sensor, itsassociated wiring, etc.), decreased weight, and increased reliability.Conventional sensoriess control techniques are generally divided intotwo categories depending upon the motor speed: (1) high frequency (HF)signal injection sensoriess control (SISC), preferred for low-speedoperation, and (2) model-based sensoriess control, which is moresuitable for high-speed operation.

In conventional HF SISC, however, a sufficient saliency ratio betweenthe d- and q-axes (e.g., inductance variation at the axes, orL_(d)/L_(q), where L_(d) is the inductance in the d-axis where the rotoris aligned with the magnetic poles and L_(q) is the inductance in theq-axis where the rotor is aligned with the gaps) should be guaranteedfor stable position estimation because position error information in thecurrent response weakens as the saliency ratio decreases and disappearsat a critical point (where L_(d)=L_(q)). Thus, conventional HF SISClimits the operating region and the motor torque capability based on thesaliency ratio, which has an inverse relationship with the loadcondition under a base speed. This limitation could be problematic,however, for certain applications, such as an engine starting/crankingmotor and a low-temperature oil pump, where a peak torque of the motoris required for a short time at the starting and initial motoroperation. One conventional approach to overcome this limitation ismodifying the motor design, which is costly and complex.

Another conventional approach to overcome this limitation ismodification of the HF SISC control strategy. The latter, for example,utilizes multiple complex look-up tables (LUTs) to modify a convergencepoint of a position error signal and an injection angle based on themotor operating point. Accordingly, improved sensorless positionestimation and control techniques for permanent magnet electric motorsare presented herein. These techniques focus on improved low-speed HFSISC sensorless drive. While these techniques may be particularlybeneficial during low speed, high torque operation, these techniquescould also be applied in all situations (e.g., low speed, low torque).This could avoid, for example having to make an estimation/controlstrategy transition as the torque increases past a torque threshold. Thetechniques of the present disclosure are simpler than the conventionaltechniques described above due to the ability to determine the d-qcurrent references from a one-dimensional table without any additionalLUTs for compensation. This simplicity allows for decreasedprocessor/memory requirements, thereby saving costs and potentiallyincreasing estimation speed.

Referring generally now to FIG. 2, an example control architecture 200for the sensorless position estimation and control techniques of thepresent disclosure is illustrated. This control architecture, forexample, could be implemented at controller 128. As shown, a pulsatingsquare-wave voltage is injected for SISC having a magnitude andfrequency of V_(h) and f_(h), respectively. When the HF referencevoltages are defined by Equation (1) below, the current variation can bederived by Equation (2) below in the estimated rotor reference framewhere two sample delay by digital control has been considered:

$\begin{matrix}{\mspace{79mu}{{\begin{bmatrix}{{v_{dsh}^{\hat{r}}}^{*}\lbrack n\rbrack} \\{{v_{dsh}^{\hat{r}}}^{*}\lbrack n\rbrack}\end{bmatrix} = \begin{bmatrix}{V_{h} \cdot {{clk}\lbrack n\rbrack}} \\0\end{bmatrix}},{and}}} & (1) \\{\begin{bmatrix}{\Delta\;{i_{ds}^{\hat{r}}\lbrack n\rbrack}} \\{\Delta\;{i_{qs}^{\hat{r}}\lbrack n\rbrack}}\end{bmatrix} = {{\frac{V_{h}T_{s}{{clk}\left\lbrack {n - 2} \right\rbrack}}{{L_{dsh}L_{qsh}} - L_{dqsh}^{2}}\begin{bmatrix}{{\Sigma\; L_{sh}} - {\Delta\; L_{sh}\cos\; 2\;{\overset{\sim}{\theta}}_{r}} + {L_{dqsh}\sin\; 2\;{\overset{\sim}{\theta}}_{r}}} \\{{{- \Delta}\; L_{sh}\sin\; 2\;{\overset{\sim}{\theta}}_{r}} - {L_{dqsh}\cos\; 2\;{\overset{\sim}{\theta}}_{r}}}\end{bmatrix}}.}} & (2)\end{matrix}$where clk[n] refers to an alternating clock signal between −1 and 1 withthe frequency of f_(h) and {tilde over (θ)}_(r) represents a positionestimation error defined as the difference between the real rotorposition, θ_(r), and the estimated position, {circumflex over (θ)}_(r).Also, T_(s) represents a sampling period andΣL_(sh)≡(L_(dsh)+L_(qsh))/2, ΔL_(sh)≡(L_(dsh)−L_(qsh))/2. In Equation(2), it should be noted that L_(qdsh) is replaced by Ldqsh because theyare mathematically the same.

After the HF signal, V_(dqsh) ^({circumflex over (r)})*, is injectedonto a fundamental component, V_(dqsf) ^({circumflex over (r)})*, anestimated position error, {tilde over (θ)}_(rest), is fed into aposition and speed estimator. Here, the estimated position error can beobtained by dividing Δi_(qs) ^({circumflex over (r)}) by the estimatedI_(Δ)·clk[n] in Equation (3) below:Δi _(qs) ^({circumflex over (r)})[n]=i _(sig) ·clk[n├2]=I _(Δ)sin(2{tilde over (θ)}_(r)−2ϕΔ)·clk[n−2]  (3),where i_(sig) corresponds to I_(Δ) sin(2{tilde over (θ)}_(r)−2Ø_(Δ)) andI_(Δ) and ♦_(Δ) are defined by Equations (4) and (5) below:

$\begin{matrix}{{I_{\Delta} = \frac{V_{h}T_{s}\sqrt{{\Delta\; L_{sh}^{2}} + L_{dqsh}^{2}}}{{L_{dsh}L_{qsh}} - L_{dqsh}^{2}}},{and}} & (4) \\{{\phi_{\Delta} = {\frac{1}{2}a\;\tan\; 2\left( {L_{dqsh},{{- \Delta}\; L_{sh}}} \right)}},} & (5)\end{matrix}$where the various L-terms represent are from a Jacobian matrix of d- andq-axes flux to d- and q-axes current.

By the estimation principle of the estimator, resulting positionestimation error in steady state can be calculated by Equation (6)below:

$\begin{matrix}{{\overset{\sim}{\theta}}_{r} = \left\{ {\begin{matrix}\phi_{\Delta} & \left( {I_{m} < I_{c}} \right) \\{\frac{1}{2}\left\lbrack {{180{^\circ}} + {2\phi_{\Delta}}} \right\rbrack}_{- \pi}^{\pi} & \left( {I_{m} > I_{c}} \right)\end{matrix},} \right.} & (6)\end{matrix}$where I_(m) and I_(c) represent the magnitude of the current at theoperating point and that of the current at the critical point,respectively. Also, [x]_(m) ^(n) means that the variable x is boundedfrom m to n. The relationship in Equation (6) can be derived byreplacing the sin(2{tilde over (θ)}_(r)−2ϕ_(Δ)) term in Equation (3)with zero.

Using Equations (5) and (6), the effect of cross-coupling inductance,L_(dqsh), can be discussed. That is, smaller L_(dqsh) at the operatingpoint would result in smaller {tilde over (θ)}_(r). For example, {tildeover (θ)}_(r) would be zero is there were no L_(dqsh), Also, it can benoted that 2ϕ_(Δ) in the region over the critical point has a magnitudeclose to 180 degrees. Therefore, in this case, {tilde over (θ)}_(r) canbe kept small if it is determined for 2{tilde over (θ)}_(r)−2ϕ_(Δ) to be+/−180 degrees. Even if it seems that this operating point is unstablebecause directions of {tilde over (θ)}_(r) and i_(sig) are reversed, itwill be disclosed that it can be a stable point if a condition thatdepends on the design characteristics is satisfied.

Estimation of the expected position error using Equation (6), however,is different with the actual position error. This because the simplecalculation of Equation (6) using dynamic inductances cannot considerclosed-loop sensorless operation. Since L_(dqsh) and ΔL_(sh) are thefunction of d- and q-axes current and θ_(r), {tilde over (θ)}_(r) in thesteady state continuously varies while the operating point moves to astable convergence point. As previously mentioned herein, previoustechniques aim to compensate for this by adding the calculated ormeasured position error to the input to cancel out the error resultedfrom cross-coupling and harmonic inductances. These techniques, however,achieve this by using multiple complex LUTs (see dashed box/lines) forcompensation at the input to the position and speed estimator inaddition to a complex maximum torque per amp (MTPA) table (see dashedbox/lines).

Referring now to FIGS. 3A-3B and with continued reference to FIG. 2,plots of the performance of the compensation-based techniques describedabove (left) and fixed reference current angle technique techniques ofthe present disclosure (right) are illustrated. These plots illustratethe position estimation stability of the estimation techniques of thepresent disclosure compared to those of the conventional estimationtechniques. As shown in the left plot, at 100% torque, the convergencesignal (the lower of the two lines) never crosses zero. In contrast, asshown in the right plot, at 100% torque, the convergence signal(initially the upper line, then the lower line) crosses zero therebygiving robust convergence. In other words, the MTPA torque commandsprovide the most efficient operation but are unstable and thus not asolution at high torque levels, even with the compensation performed byconventional techniques. The techniques of the present disclosureachieve the peak torque requirements by shifting the commanded currentto provide stable operation with minimal efficiency sacrifice.

Referring again to FIG. 2, a simple LUT replaces the complex MTPA tableto determine a current magnitude reference I_(m)*; based on the torquereference T_(e)*. Further, if the system does not require accuratetorque control, the LUT can be, eliminated altogether and the referencecan be generated sir ply regulating I_(m)*. A reference current angle β*represents the difference between the angle of current vector and theestimate q-axis. In the techniques of the present disclosure, thereference current angle β* is fixed as a constant. Thus enables the LUTin FIG. 2 to be half of the size of the conventional MTPA table. Thecriticality in the techniques of the present disclosure is selecting theappropriate value for the reference current angle β*.

In determining the value for β*, stability and MTPA tracking should besimultaneously considered. For stable operation, i_(sig) by {tilde over(θ)}_(r) should have positive slope at the point of i_(sig)=0. Also β*should satisfy Equation (7) below for the actual current in the rotorreference frame to operate on the MTPA trajectory:2{tilde over (θ)}_(r)−2ϕΔ=2(β*−β_(MTPA))−2ϕ_(Δ,MTPA)=0° or ±180°  (7)In the above, 0 degrees or 180 degrees is determined by I_(m).Therefore, proper β* to operate on the MPTA trajectory can be obtainedfrom Equation (7) using the data on the operating point. Unstable pointswith a negative slope at i_(sig)=0 can be removed. It could be impliedthat β* should have a different value according to {tilde over (θ)}_(r)for MTPA tracking. However, this is impractical because thediscontinuity differs in every {tilde over (θ)}_(r). Moreover, animproper β* in the region over the discontinuity may lead toinstability. Thus, when this fixed β* control scheme is used, onlyI_(m)* is determined from the LUT to generate the desired T_(e)*. Thisrelationship between T_(e)* and I_(m)* could be extracted, for example,by actual experiment using a torque sensor or finite element analysis(FEA).

Referring now to FIG. 4, a flow diagram of an example method 400 ofsensorless position estimation and control of a permanent magnetelectric motor (e.g., motor 104) is illustrated. It will be appreciatedthat the various steps described below could be performed by controller128, by another controller, or some combination thereof. At 404, themethod 400 determines whether the motor speed (e.g., measured by sensor120) is less than a threshold. This threshold could be indicative oflow-speed operation such that the control techniques of the presentdisclosure are necessary in order to achieve full torque demand.

As previously mentioned, however, this method 400 may not be limited toonly certain operation regions, such as low speed, high torque. Instead,the method 400 could be applicable to all operating regions (e.g., lowspeed, low torque). This could avoid, for example having to make anestimation/control strategy transition (from conventional techniques tothe disclosed techniques) as the torque increases past a torquethreshold, which could cause a delay or otherwise increase complexity.Thus, step 404 can be considered optional or specific to only applyingthe method 400 during low speed, high torque operation.

When 404 is false, the method 400 proceeds to 408 where backelectro-motive force (EMF) estimation is performed and the method 400proceeds to 424. When 404 is true, the method 400 proceeds to 412 wherethe current commands i_(dqs) ^({circumflex over (r)})* are selected toachieve the commanded torque T_(e)* with stable position estimation asdescribed above (i.e., fixed β*, I_(M) determined to achieve T_(e)*using LUT). It will be appreciated that step 412 could also involve acondition check for stable operation as previously described herein. At416, the method 400 injects the high frequency voltage (V_(dqsh)^({circumflex over (r)})*; see FIG. 2). At 420, the method 400 extractsthe position estimate ({circumflex over (θ)}_(r); see FIG. 2). At 424,the method 400 regulates the motor current based on the estimatedposition and the estimated back-EMF, if applicable. The method 400 thenreturns to 404 and repeats.

It will be appreciated that the term “controller” as used herein refersto any suitable control device or set of multiple control devices thatis/are configured to perform at least a portion of the techniques of thepresent disclosure. Non-limiting examples include anapplication-specific integrated circuit (ASIC), one or more processorsand a non-transitory memory having instructions stored thereon that,when executed by the one or more processors, cause the controller toperform a set of operations corresponding to at least a portion of thetechniques of the present disclosure. The one or more processors couldbe either a single processor or two or more processors operating in aparallel or distributed architecture.

It should be understood that the mixing and matching of features,elements, methodologies and/or functions between various examples may beexpressly contemplated herein so that one skilled in the art wouldappreciate from the present teachings that features, elements and/orfunctions of one example may be incorporated into another example asappropriate, unless described otherwise above.

What is claimed is:
 1. A powertrain system for a vehicle, the powertrainsystem comprising: a permanent magnet electric motor configured togenerate drive torque for propulsion of the vehicle; and a controllerconfigured to: perform sensorless position estimation on the permanentmagnet electric motor across all load/torque operating regions by: (i)determining a reference torque to be achieved by the electric motorbased on a set of vehicle operating parameters, (ii) determining areference current magnitude to achieve the determined reference torqueusing a first maximum torque per amperage (MTPA) table, (iii) selectinga fixed reference current angle that simultaneously satisfies stabilityand MTPA tracking constraints, wherein the fixed reference current angleprovides for a smaller sized first MTPA table and eliminatesestimation/control strategy transitions across different load/torqueoperating regions, (iv) determining current commands for the electricmotor based on the determined reference current magnitude and the fixedreference current angle, and (v) injecting a high frequency voltage intoa voltage control loop for the electric motor and estimating a positionof a rotor of the electric motor thereafter; and control a currentprovided to the electric motor based on the determined current commandsand the estimated rotor position.
 2. The system of claim 1, wherein thecontroller determines the current commands for the electric motor toachieve the determined reference torque without utilizing a larger andmore complex second MTPA table.
 3. The system of claim 1, wherein thecontroller obtains a compensation value that is applied to an estimatedrotor position error without utilizing multiple complex look-up tables(LUTs).
 4. The system of claim 1, wherein the determining of thereference current magnitude and the current commands based on thedetermined reference current magnitude and the fixed reference currentangle are performed across all possible values of the determinedreference torque so as to not require an estimation/control strategytransition.
 5. The system of claim 1, wherein the controller does notutilize a position sensor to measure an actual position of the rotor. 6.A sensorless position estimation and control method for a permanentmagnet electric motor of a powertrain system of a vehicle, the methodcomprising: performing, by a controller of the powertrain system,sensorless position estimation on the permanent magnet electric motoracross all load/torque operating regions by: determining, by thecontroller, a reference torque to be achieved by the electric motorbased on a set of vehicle operating parameters; determining, by thecontroller, a reference current magnitude to achieve the determinedreference torque using a first maximum torque per amperage (MTPA) table;selecting, by the controller, a fixed reference current angle thatsimultaneously satisfies stability and MTPA tracking constraints,wherein the fixed reference current angle provides for a smaller sizedfirst MTPA table and eliminates estimation/control strategy transitionsacross different load/torque operating regions; determining, by thecontroller, current commands for the electric motor based on thedetermined reference current magnitude and the fixed reference currentangle; and injecting, by the controller, a high frequency voltage into avoltage control loop for the electric motor and estimating, by thecontroller, a position of a rotor of the electric motor thereafter; andcontrolling, by the controller, a current provided to the electric motorbased on the determined current commands and the estimated rotorposition.
 7. The method of claim 6 wherein determining the currentcommands for the electric motor to achieve the determined referencetorque is performed without utilizing a larger and more complex secondMTPA table.
 8. The method of claim 6, wherein obtaining a compensationvalue that is applied to an estimated rotor position error is performedwithout utilizing multiple complex look-up tables (LUTs).
 9. The methodof claim 6, wherein the determining of the reference current magnitudeand the current commands based on the determined reference currentmagnitude and the fixed reference current angle are performed across allpossible values of the determined reference torque so as to not requirean estimation/control strategy transition.
 10. The method of claim 6,wherein the controller does not utilize a position sensor to measure anactual position of the rotor.